I spent a bit of time modeling reliability of engineering systems - so it looks like we've chewed some of the same turf (although I suspect I took smaller bites!). I greatly appreciate the short technical overview as it captures something of what I've been trying to get at regarding randomness and predictability.

Let me say that when making reference to "randomness within limits" I did, actually, have the notion of a probability distribution in mind on two accounts;

First, probability theory is a relatively recent notion (if one can call Pascal and Fermat "modern"!) and it was precisely one of the issues I had in mind when I questioned whether classical philosophical/theological notions of "chance" ought to constrain out reflections. I'd humbly suggest that attempting a treatment of the notion of chance without reference to probability theory may be problematic.

Second, I've often wanted to respond to claims of "chance" in evolution with "Ah, yes, but what SORT of chance" - but I doubt that the folk we've been making reference to (Dawkins, Gould, Coyne, etc) would get the point! But I'm glad to see somebody sees the point that even in a random system, some outcomes may be more likely than others - even randomness has its constraints.

Blessings,
Murray

Iain Strachan wrote:
> Hi, Murray,
>
> you wrote:
> Now, personally, I'm not sure that "chance" should mean "all outcomes
> are equally likely" hence I've employed the phrase "randomness within
> limits".
>
> I like what you're saying here. Since my own academic area is
> probabilistic modelling, I agree wholeheartedly, though instead of
> "randomness within limits" I would use the term "probability
> distribution". These can be modelled mathematically with what is called
> a "probability density function" & the major part of the development
> work I do is developing probability density functions based on empirical
> data. The case of "all outcomes are equally likely" is a special case
> of a probability distribution, known as a "uniform distribution". This
> only applies to discrete outcomes such as the toss of a die. In the
> case of continuous variables, we have the "normal distribution" (the
> bell-shaped curve known as the Gaussian distribution), characterised by
> the mean and standard deviation. I work with mixtures of Gaussian
> distributions in multi-dimensional space, which has applications in
> areas as diverse as jet engine health monitoring, and analysis of
> Electrocardiogram waveforms.
>
> But the example I like to give of randomness with a definite outcome is
> much simpler. When you pull the plug out of the bath, nearly all the
> water goes down the plug-hole, despite the fact that the motion of the
> individual molecules appears random - it will be Brownian motion with a
> drift, or bias applied to it.
>
> Regards
> Iain

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Received on Wed Apr 29 04:56:24 2009